The new Fore and Aft Marina is to be located on the Ohio River near Madison, Indiana. Assume that Fore and Aft decides to build a docking facility where one boat at a time can stop for gas and servicing.Assume that arrivals follow a Polsson probability distribution, with an arrival rate of 8 boats per hour, and that service times follow an exponential probability distribution, with a service rate of 10 boats per hour.The manager of the Fore and Aft Marina wants to investigate the possibility of enlarging the docking facility so that two boats can stop for gas and servicing simultaneously.Note: Use Po values from Table 11.4 to answer the questions below.a. What is the probability that the boat dock will be idle? Round your answer to four decimal places.P₂ =b. What is the average number of boats that will be waiting for service? Round your answer to four decimal places.Lg=W₂c. What is the average time a boat will spend waiting for service? Round your answer to four decimal places.)0.4000 hours-0.20003.2000d. What is the average time a boat will spend at the dock? Round your answer to four decimal places.YesW = 0.5000 hourse. If you were the manager of Fore and Aft Marina, would you be satisfied with the service level your system will be providing?Why or why not? Round your answers to whole numbers.Because the average wait time isWq=Pete's Market is a small local grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane according to a Poisson probability distribution, with an arrival rate of 15 customers perhour. The checkout service times follow an exponential probability distribution, with a service rate of 25 customers per hour. The manager's service goal is to limit the waiting time prior to beginning the checkoutprocess to no more than five minutes. Also the manager of Pete's Market wants to consider one of the following alternatives for improving service. Calculate the value of W, for each alternative.a. Hire a second person to bag the groceries while the cash register operator is entering the cost data and collecting money from the customer. With this improved single-server operation, the service rate could beincreased to 32 customers per hour. Round your answer to three decimal places. Do not round intermediate calculations.1.654 minutesseconds. Each channel is idle0.237 minutesb. Hire a second person to operate a second checkout counter. The two-server operation would have a service rate of 25 customers per hour for each server. Note: Use Po values from Table 11.4 to answer thisquestion. Round your answer to three decimal places. Do not round intermediate calculations.Wq=1What alternative would you recommend? Justify your recommendation.% of the time.Recommend two checkout counters with two employeesThe two counter system (has better service but costs morehas better service and is cheaperhas worse service but is cheaperhas worse service and costs more All airplane passengers at the Lake City Regional Airport must pass through a security screening area before proceeding to the boarding area. The airport has three screening stations available, and the facility manager must decide how many tohave open at any particular time. The service rate for processing passengers at each screening station is 3.5 passengers per minute. On Monday morning the arrival rate is 4.9 passengers per minute. Assume that processing times at eachscreening station follow an exponential distribution and that arrivals follow a Poisson distribution.Note: Use Po values from Table 11.4 to answer the questions below.a. Suppose two of the three screening stations are open on Monday morning. Compute the operating characteristics for the screening facility.Round your answer to four decimal places.Po =Round your answers to two decimal places.La =L=W₂ =W =PwRound your answer to four decimal places.b. Because of space considerations, the facility manager's goal is to limit the average number of passengers waiting in line to 10 or fewer. Will the two-screening-station system be able to meet the manager's goal?yes or no?c. What is the average time required for a passenger to pass through security screening? Round your answer to two decimal places.Po =The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with an arrival rate of 8 requests per hourcan be used to describe the arrival pattern and that service times follow an exponential probability distribution with a service rate of 11 requests per hour.mina. What is the probability that no requests for assistance are in the system? If required, round your answer to four decimal places.Lg =minminb. What is the average number of requests that will be waiting for service? If required, round your answer to four decimal places.Wq =c. What is the average waiting time in minutes before service begins? If required, round your answer to nearest whole number.W =Pw=)d. What is the average time at the reference desk in minutes (waiting time plus service time)? If required, round your answer to nearest whole number.minmine. What is the probability that a new arrival has to wait for service? If required, round your answer to four decimal places.

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The new Fore and Aft Marina is to be located on the Ohio River near Madison, Indiana. Assume that Fore and Aft decides to build a docking facility where one boat at a time can stop for gas and servicing. Assume that arrivals follow a Polsson probability distribution, with an arrival rate of 8 boats per hour, and that service times follow an exponential probability distribution, with a service rate of 10 boats per hour. The manager of the Fore and Aft Marina wants to investigate the possibility of enlarging the docking facility so that two boats can stop for gas and servicing simultaneously. Note: Use Po values from Table 11.4 to answer the questions below. a. What is the probability that the boat dock will be idle? Round your answer to four decimal places. Pg= b. What is the average number of boats that will be waiting for service? Round your answer to four decimal places. Lg= W₂ 0.2000 c. What is the average time a boat will spend waiting for service? Round your answer to four decimal places. 0.4000 hours d. What is the average time a boat will spend at the dock? Round your answer to four decimal places. W = 3.2000 Yes 0.5000 hours e. If you were the manager of Fore and Aft Marina, would you be satisfied with the service level your system will be providing? Why or why not? Round your answers to whole numbers.

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...